| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
What is \( 7 \)\( \sqrt{63} \) + \( 9 \)\( \sqrt{7} \)
| 63\( \sqrt{7} \) | |
| 16\( \sqrt{441} \) | |
| 30\( \sqrt{7} \) | |
| 63\( \sqrt{63} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{63} \) + 9\( \sqrt{7} \)
7\( \sqrt{9 \times 7} \) + 9\( \sqrt{7} \)
7\( \sqrt{3^2 \times 7} \) + 9\( \sqrt{7} \)
(7)(3)\( \sqrt{7} \) + 9\( \sqrt{7} \)
21\( \sqrt{7} \) + 9\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
21\( \sqrt{7} \) + 9\( \sqrt{7} \)a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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commutative property for division |
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distributive property for division |
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distributive property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
If a car travels 45 miles in 1 hour, what is the average speed?
| 65 mph | |
| 30 mph | |
| 70 mph | |
| 45 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 30% off." If Roger buys two shirts, each with a regular price of $42, how much will he pay for both shirts?
| $12.60 | |
| $29.40 | |
| $71.40 | |
| $46.20 |
By buying two shirts, Roger will save $42 x \( \frac{30}{100} \) = \( \frac{$42 x 30}{100} \) = \( \frac{$1260}{100} \) = $12.60 on the second shirt.
So, his total cost will be
$42.00 + ($42.00 - $12.60)
$42.00 + $29.40
$71.40
What is (a4)5?
| a20 | |
| a-1 | |
| a9 | |
| 4a5 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(a4)5